Finite Group Databasebeta

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C3×C5×C31×Dic15 #42124661

order27900
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C31 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C31×Dic15
unambiguous semidirect productC3⋊(C3×C5×Dic5×C31)

Splittings

derivedC3×C5 ⋊ C3×C4×C5×C31
HallC32×C52×C31 ⋊ C4
HallC52×C31 ⋊ C3×Dic3
HallC32×C31 ⋊ C5×Dic5
HallC32×C52 ⋊ C4×C31
SylowC52 ⋊ C3×Dic3×C31
SylowC32 ⋊ C5×Dic5×C31

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C31D15
commutator, hypocenterC3×C5C3×C4×C5×C31
FrattiniC2C3×C5×D15×C31
Fitting, socle, prime radicalC2×C32×C52×C31C2
cosocleC2×C3×C5C2×C3×C5×C31
LCSG ▷ C3×C5
UCSC1 ◁ C2×C3×C5×C31

160 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Conjugacy classes & character table

8370 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 408);